Generally speaking, racing is a spring, summer and fall sport. Usually things start in the early spring, and finish up by the end of October. The most notable exception to this is the World Rally Championship, which traditionally starts with The Monte Carlo Rally in January (!), and ends with the Rally Great Britain in November.
NASCAR has the highest number of races in a season (36), while most race seasons run in the 16 to 20 race a year range.
What follows are representative season schedules for well known racing series.